To solve the problem, we need to analyze the assertion and the reason provided in the question.
### Step-by-Step Solution:
1. **Understanding the Assertion**:
- The assertion states that a particle is rotating in a circle of radius 1 m, and at a given instant, its speed is 2 m/s. It claims that the acceleration of the particle at that instant is 4 m/s².
2. **Identifying Types of Acceleration**:
- In circular motion, the total acceleration of a particle can be divided into two components:
- **Centripetal Acceleration (a_c)**: This is directed towards the center of the circle and is given by the formula:
\[
a_c = \frac{v^2}{r}
\]
- **Tangential Acceleration (a_t)**: This is due to the change in the speed of the particle along the circular path.
3. **Calculating Centripetal Acceleration**:
- Given:
- Speed (v) = 2 m/s
- Radius (r) = 1 m
- Now, substituting the values into the centripetal acceleration formula:
\[
a_c = \frac{(2 \, \text{m/s})^2}{1 \, \text{m}} = \frac{4 \, \text{m}^2/\text{s}^2}{1 \, \text{m}} = 4 \, \text{m/s}^2
\]
- Therefore, the centripetal acceleration at that instant is indeed 4 m/s².
4. **Analyzing Tangential Acceleration**:
- The assertion claims that the total acceleration of the particle is 4 m/s². However, we have only calculated the centripetal acceleration.
- To determine the total acceleration, we would need information about the tangential acceleration, which is not provided in the question.
5. **Conclusion on Assertion**:
- Since the assertion states that the total acceleration is 4 m/s² without considering the tangential acceleration, we cannot confirm it as true. Therefore, the assertion is **false**.
6. **Conclusion on Reason**:
- The reason states that the centripetal acceleration at this instant is 4 m/s² towards the center of the circle, which we have confirmed to be true.
### Final Evaluation:
- The assertion is false, and the reason is true. Therefore, the correct conclusion is that the assertion is false while the reason is true.
